Confidence Interval Calculator
Find the confidence interval for a population mean — enter the sample mean, standard deviation and size, then pick 90%, 95% or 99% confidence.
Reviewed by the OmniCalc teamMethod verified 2026-07-01
100 ± 5.36768
= [94.6323, 105.368]
Confidence interval 94.6323 to 105.368Show steps
- At 95% confidence, the z-score is z = 1.96.
- Standard error: SE = s ÷ √n = 15 ÷ √30 = 2.738613.
- Margin of error: E = z × SE = 1.96 × 2.738613 = 5.367681.
- Confidence interval: x̄ ± E = 100 ± 5.367681 = [94.632319, 105.367681].
How to use the confidence interval calculator
- 1Enter the sample mean (x̄) and standard deviation (s).
- 2Set the sample size (n) and choose 90%, 95% or 99% confidence.
- 3Read the interval and margin of error, with the formula under Show steps.
Wider interval, higher confidence
To be more confident, you accept a wider interval: 99% uses z = 2.576 and 95% uses z = 1.96, so raising the confidence level stretches the range around the mean. A larger sample size (n) does the opposite — it shrinks the margin of error, because the standard error s ÷ √n falls as n grows.
Frequently asked questions
What is a confidence interval?
A confidence interval is a range around the sample mean that is likely to contain the true population mean. A 95% interval means that if you repeated the sampling many times, about 95% of the intervals built this way would capture the population mean.
Which z-score matches each confidence level?
This calculator uses z = 1.645 for 90%, z = 1.96 for 95% and z = 2.576 for 99% confidence. A higher confidence level uses a larger z, which widens the interval around the mean.
What formula does this use?
The interval is x̄ ± z × (s ÷ √n), where x̄ is the sample mean, s the sample standard deviation and n the sample size. The part after the ± is the margin of error. It uses the normal (z) approximation, which is best for larger samples (n ≥ 30) or a known population standard deviation; smaller samples use the t-distribution.